The function and accuracy of most mixed-signal circuits all heavily rely on the open-loop gains of the operational amplifiers (OPAMPs) in them. Unfortunately the open-loop gains of the OPAMPs are very vulnerable to process variation. Sometimes, even the SPICE (Simulation Program with Integrated Circuit Emphasis) simulation results could not precisely predict what the open-loop gains will be. As a result, accurately measuring the OPAMPs' open-loop gains is important for diagnosing the prototype circuits as well as for production tests.
Traditionally, the open-loop gains are measured with an expensive network analyzer and a tedious testing setup. Modern SOC ICs usually contain tens of OPAMPs which can not drive such heavy off-chip loads. Furthermore, the limited observation pins makes measuring the embedded OPAMPs' open-loop gains being troublesome and costly.
Please refer to the article proposed by G. Giustolisi and G. Palumbo, “An approach to test the open-loop parameters of feedback amplifier”, IEEE Trans. On Circuits and Systems I, Vol. 49, No. 1, pp. 70-75, January 2002. The test approach requires a costly network analyzer to measure the phase and magnitude responses of the feedback amplifier made of the operational amplifier under test (OPAUT) to derive the open-loop gain. This method may not be applied to test the OPAUT in an SOC chip due to the limited driving capability of the OPAUT and limited observation nodes of the chip. Besides, it assumes the transfer function of the OPAUT has only two-poles which may not be true. More than two poles in the transfer function of the OPAUT may lead to significant measurement errors.
Please further refer to the article proposed by K. Arabi and B. Kaminska, “Design for Testability of Embedded Integrated Operational Amplifiers”, IEEE JSSC, Vol. 33, No. 4, pp. 573-581, April 1998, which disclosed a design for measuring embedded operational amplifier. The authors proposed a method to estimate the gain-bandwidth product of the OPAUT by reconfiguring the OPAUT, auxiliary resistors, and capacitors as an oscillator. Under some assumptions, the gain-bandwidth product of the OPAUT can be derived by observing the oscillation frequency. This method does not require a costly network analyzer; however, it can not measure the open-loop gain of the OPAUT. Beside, its result is sensitive to the parasitic capacitance of the circuits since the parasitic capacitance would change the oscillation frequency.
Please further refer to the book, “An introduction to mixed-signal IC test and measurement”, written by M. Burns and G. W. Roberts and published in 2001 by Oxford University, in which a method for measuring the characteristics of amplifier is disclosed in pages 68 & 69. Moreover, W. M. C. Sansen, M. Steyaert and P. J. V. Vandeloo have disclosed “Measurement of operational amplifier characteristics in the frequency domain”, IEEE Trans. On instrumentation and measurement, Vol. IM-34, No. 1, pp. 59-64, May, 1985. The above-mentioned two traditional measurement methods require an expensive and precise analog stimulus generator, voltage meter, as well as the auxiliary amplifier. It also requires a huge resistance spread (approximating the open-loop gain). Thus, it is not suitable for embedded implementation.
In accordance with the part of conventional first-order Sigma-Delta modulator, its basic theory and disadvantage are described as follows. Please refer to the block diagram shown in FIG. 1a, which includes a subtractor, a loop filter 1, an A/D converter 2 and a D/A converter 3. FIG. 1b shows the corresponding linear model of FIG. 1a. In terms of the z-domain, the following equation can be derived:
                              Y          ⁡                      (            z            )                          =                                                            H                ⁡                                  (                  z                  )                                                            1                +                                  H                  ⁡                                      (                    z                    )                                                                        ⁢                          X              ⁡                              (                z                )                                              +                                    1                              1                +                                  H                  ⁡                                      (                    z                    )                                                                        ⁢                          E              ⁡                              (                z                )                                                                        (        1        )            where Y(z) is the output function, X(z) is the input function, H(z) is the discrete-time transfer function of the loop filter, and E(z) is the quantization error generated by the first-order Sigma-Delta modulator.Eq. (1) can be generalized and expressed as the following equation:Y(z)=STF(z)X(z)+NTF(z)E(z)  (2)where STF(z) and NTF(z) are defined as the signal transfer function (STF) and noise transfer function (NTF) of a Sigma-Delta modulator respectively. For the example shown in FIG. 1a, the STF and NTF can be shown to be
                              S          ⁢                                          ⁢          T          ⁢                                          ⁢                      F            ⁡                          (              z              )                                      =                              H            ⁡                          (              z              )                                            1            +                          H              ⁡                              (                z                )                                                                        (        3        )                                          N          ⁢                                          ⁢          T          ⁢                                          ⁢                      F            ⁡                          (              z              )                                      =                  1                      1            +                          H              ⁡                              (                z                )                                                                        (        4        )            If the STF(z) is designed to have the characteristics of a low-pass or an all-pass filter and the NTF(z) is designed to have the characteristics of a high-pass filter, it is known from Eq. (3) and (4) that most of quantization noise will be shifted to the high-frequency range after the input signal X(z) has been processed by the Sigma-Delta modulation. As a result, the quantization noise left within the base band range of signal will be greatly reduced. The shaped high-frequency quantization noise could be filtered out by using a digital low-pass filter. An example to achieve the objectives is choosing
                                          H            ⁡                          (              z              )                                =                                    1                              z                -                1                                      =                                          z                1                                            1                -                                  z                  1                                                                    ,                            (        5        )            that is, exerting an integrator as the loop filter.
Detailed circuit analysis indicates that under some proper test setting, the gain error of the first-order Sigma-Delta modulator is mainly determined by the open-loop gain of the operational amplifier that constitutes the integrator. Hence, if the gain error of the first-order Sigma-Delta modulator could be accurately measured, the open-loop gain of the operational amplifier could be calculated accordingly. The input portion of conventional Sigma-Delta modulator can not but accepts analog signals as its inputs, while analog signals are hard to be precisely controlled and are prone to be disturbed by the test setting and environmental noise. Hence, using analog signals to perform the gain error test shall employ the analog signal source that can be precisely controlled. Such high-quality signal source usually could be provided by high-end test equipment only. Besides, how to prove that the test setting and testing environment won't result in additional errors is again a hard nut to crack. Therefore, using analog signals to test the open-loop gain of the OPAUT has not only higher difficulty but also higher cost.
To improve the shortcomings of the aforementioned prior arts and precisely measure the open-loop gain of the operational amplifier, the present invention specifically discloses a first-order Sigma-Delta modulator composed of simple components including an OPAUT, a plurality of switches, a plurality of capacitors, an A/D converter, and a plurality of DC voltage sources, and particularly specifies a device that could use purely digital stimuli to precisely measure the open-loop gain of the OPAUT.
The first object of the present invention is to provide a device that could be utilized to measure the open-loop gain of the OPAUT with a single-ended output or differential-ended output.
The second object of the present invention is to provide a first-order Sigma-Delta modulator which is reconfigured by a plurality of switches, a plurality of capacitors, an A/D converter, an OPAUT and a digital circuit, and can receive at least one or more digital input stimulus signals in a test mode.
The third object of the present invention is to provide a first-order Sigma-Delta modulator which is constructed by a plurality of switches, a plurality of capacitors, an A/D converter, an OPAUT, and a digital circuit and can receive one or more digital input stimulus signals.